ABSTRACT

At any rate, most of the attempts to do the impossible have called upon infinity in one way or another: not necessarily the infinitely large, not necessarily the infinitely small but certainly the infinitely many. An "ideal number" is represented by an infinite set of actual numbers, and an illusory finite object—the tribar—is represented by an actual infinite object, a periodic bar. A countable set is infinite, but only "potentially" so, because each member appears at some finite stage. One need not try to grasp all members of the set simultaneously—just the process for producing them. The infinite paths are interesting because they correspond to points in the Cantor set. The real numbers are equally important as a basis for the limit concept in calculus, the key to the modern approach which avoids the contradictory aspects of infinitesimals.